From Right: New Dutch King Willem-Alexander, his mother, Her Royal Highness Princess Beatrix, and his wife Queen Maxima appear on the balcony of the Royal Palace at the Dam Square in Amsterdam April, 30 2013.

The last time the Dutch installed a new monarch, exactly 33 years ago, it was a riot — literally. Protesters overran the streets not to greet their new Queen Beatrix, but to demand affordable housing. “Geen woning, geen kroning” — no accommodation, no coronation — they chanted. Today’s program of events marking the abdication of the Queen and the investiture as King of her son, Willem-Alexander, is unlikely to pass off without some protests. Dutch republican groups are encouraging supporters to wear white clothes or hang white sheets from their windows to dilute the “orange madness,” as throngs of their compatriots flood Amsterdam decked in the signature color of the royal House of Orange to celebrate its latest crowned head.

The scale of the celebration indicates two things that might seem contradictory: the first is that large numbers of Dutch really care about their monarchy — and opinion polls reinforce that impression, with up to three-quarters of the population declaring themselves in favor of the institution. The second is that the monarchy no longer matters enough to attract much hostility. Last year, parliament removed from the Queen her last remaining role in national politics — appointing representatives to help with the formation of coalitions after elections. The monarch’s job is now purely ceremonial, the Ribbon Cutter in Chief to a country, which, though in better shape than many other euro-zone economies, is in the grips of austerity measures, with unemployment at an 18-year high. This might not seem the best moment for expensive displays of pomp and ceremony.

Yet the cheering, orange-clad crowds suggest otherwise. The House of Orange and Europe’s other monarchies — reigning in Belgium, Britain, Denmark, Liechtenstein, Luxembourg, Monaco, Norway, Spain and Sweden — have proved surprisingly resilient. These royals are not immune to the changes that have helped erode trust in politicians and other pillars of the establishment — far from it. They have come under ever more scrutiny, their frolics photographed through long lenses and their accounts, in some countries, put under the microscope. They have often disappointed their subjects while delighting tabloid editors. Who can forget Britain’s long-running Charles and Diana soap opera? Belgian royals are still riding out the repercussions of a controversy involving Queen Fabiola, the widow of former King Baudouin, who allegedly sought to create a private fund to shield future bequests from her estate from taxes. In 2010 Sweden’s King Carl XVI Gustaf did not deny allegations in a biography of a past affair with Camilla Henemark, the lead singer of a band called Army of Lovers. “The book came to us quite late yesterday afternoon, and I have not had time to read it yet. I cannot review a book that I have not yet read,” he said. “I have seen a few of the headlines that have not been too nice. I’ve talked with my family and the Queen. We will turn the page and go on now, because as I understand, this is about things that happened a long time ago.”

The fall from grace of Spain’s King Juan Carlos I has been especially precipitous. As his country succumbed to a deep and gloomy economic crisis last year, the monarch evinced sympathy for the rising ranks of the hopelessly unemployed and then promptly departed on an expensive private safari to shoot big game in Botswana. His ill-judged trip came as the authorities looked into alleged corruption and tax fraud involving his son-in-law Iñaki Urdangarin, a probe that later extended to the King’s daughter, Urdangarin’s wife Princess Cristina. A poll published earlier this month in the Spanish newspaper El País laid bare the cumulative impact of these events: the King’s approval rating has slipped into the negative for the first time ever, at -11 points, with 53% of respondents disapproving of the way he carries out his duties.

That 43% still expressed approval for the King is probably a reflection of his historic role in helping steer Spain to democracy after the 1975 demise of military dictator Francisco Franco and his intervention in 1981 to halt a coup. Those, admittedly, are substantial contributions. Most royals find it harder to articulate what they bring to public life. “Even what is sometimes sarcastically called ribbon cutting can be meaningful,” said the Netherlands’ Willem-Alexander, discussing what he hopes to achieve as King in a Dutch TV interview given ahead of his accession.

Celebrities cut ribbons, open supermarkets and launch ships. But monarchs, when they do their jobs well — and that means steadily and quietly and avoiding the taint of scandal and venality as Willem-Alexander’s mom and Britain’s Queen Elizabeth and Denmark’s Queen Margrethe have all managed, over multiple decades — also provide a focus of national unity. Republicans argue that elected heads of state can and should fill that role. Yet trust in politicians continues to erode faster and further than in royalty. In Spain, Prince Felipe, Juan Carlos’ son and heir, remains comparatively popular; in El País’ poll, 61% approved of Felipe against 33% who did not. That contrasts with the 93% who disapproved of all politicians.

Across Europe and beyond, institutions that used to command trust — parliaments, police, religious leaders, and don’t even mention banks — have fallen into bad odor. Countries are locked in crises, not only of economics but identity. The Dutch garbing themselves in orange and heading to Amsterdam will be cheering not only the new King but enjoying an increasingly rare opportunity to cheer themselves.